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Selection in incomplete markets and the CAPM portfolio rule

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  • Giulio Bottazzi
  • Daniele Giachini

Abstract

This paper studies whether, and to what extent, trading in an incomplete competitive market rewards the CAPM portfolio rule over alternative rules. We find that, if a mean-variance trader faces an agent who invests in each asset proportionally to expected relative payoffs, in the long-run only two scenarios are possible: either the mean-variance trader vanishes or both agents survive with fixed and constant wealth shares. In both cases, asymptotic prices are proportional to assetsù expected payoff, and the relation between prices and returns implied by the CAPM does not generally hold. Conversely, when a mean-variance trader faces a generic fixed-mix investor, several long-run outcomes are possible, such as dominance of one trader, survival of both, and generic path-dependency. We provide sufficient conditions to assess such outcomes. We find that the different outcomes can be effectively discussed in terms of the effective risk aversion of the trading strategies, as implied by their portfolio choices conditional on prevailing market prices. In general, a larger effective risk aversion constitutes a survival advantage.

Suggested Citation

  • Giulio Bottazzi & Daniele Giachini, 2020. "Selection in incomplete markets and the CAPM portfolio rule," LEM Papers Series 2020/29, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    • Handle: RePEc:ssa:lemwps:2020/29
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    References listed on IDEAS

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    4. Rabah Amir & Sergei Belkov & Igor V. Evstigneev & Thorsten Hens, 2022. "An evolutionary finance model with short selling and endogenous asset supply," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 655-677, April.
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    9. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2018. "Long-run heterogeneity in an exchange economy with fixed-mix traders," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 407-447, August.
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    1. Andrea Antico & Giulio Bottazzi & Daniele Giachini, 2022. "On the evolutionary stability of the sentiment investor," LEM Papers Series 2022/09, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.

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